Systems, methods and computer program products for modeling demand, supply and associated profitability of a good in an aggregate market

ABSTRACT

A method is provided that includes defining a plurality of independent component markets for a good. In accordance with the method, each component market can be defined a respective price sensitivity distribution of a unit purchase of the good, as well as a market potential distribution of a number of units of the good. The demand and/or supply in the aggregate market can thus then be modeled based upon the price sensitivity distributions and market potential distributions of the component markets. The method can further include modeling cost and/or profitability of the good in an aggregate market. Profitability can be modeled based upon the demand model and the cost model for the aggregate market.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation-in-part of U.S. patentapplication Ser. No. 10/453,396, entitled: Systems, Methods and ComputerProgram Products for Modeling Uncertain Future Benefits, filed on Jun.3, 2003 and published on Dec. 9, 2004 as U.S. Patent ApplicationPublication No. 2004/0249642; and U.S. patent application Ser. No.10/453,727, entitled: Systems, Methods and Computer Program Products forModeling Demand, Supply and Associated Profitability of a Good, filed onJun. 3, 2003 and published on Dec. 9, 2004 as U.S. Patent ApplicationPublication No. 2004/0249696, the contents of both of which areincorporated by reference.

FIELD OF THE INVENTION

The present invention relates generally to systems, methods and computerprogram products for modeling future demand of a good and, moreparticularly, to systems, methods and computer program products formodeling the future demand, supply and associated profitability of agood over time where the demand, supply and/or associated profitabilityare subject to uncertainty.

BACKGROUND OF THE INVENTION

In classical economics, supply and demand have traditionally beenexamined by economists to explain how markets generate the price andquantity of a traded good. Generally, markets are seen to generate theprice and quantity of a traded good by correlating the amount of a givengood that manufacturers anticipate selling at a given price (i.e.,supply) with the amount of that good that consumers are willing topurchase (i.e., demand). Supply refers to the varying amounts of acertain good that manufactures will supply at different prices. Because,in general, a higher price yields a greater supply, supply is oftenillustrated by an upward-sloping curve on a graph of price versusquantity during a specified time period. Demand, on the other hand,refers to the quantity of a good that is demanded by consumers at anygiven price. Because demand generally decreases as price increases,demand is often illustrated by a downward-sloping curve on a graph ofprice versus quantity for a specified time period.

To manufacturers, modeling demand and supply can be useful tools thatcan aid in modeling the profitability of a given good. Traditionally,manufacturers have not been capable of reliably quantifying a forecastof future demand, supply and thus profitability for projects when asignificant amount of uncertainty exists. Whereas conventionaltechniques for modeling demand, supply and profitability provideadequate models, they have shortcomings in certain, but crucial,applications. For example, such techniques are typically unable toeasily incorporate changes in uncertainty over time. Also, for example,such techniques are typically unable to easily account for contingentdecisions that may occur during a given time period.

SUMMARY OF THE INVENTION

The present invention provides systems, methods and computer programproducts for modeling demand, supply and associated profitability of agood in an aggregate market. The systems, methods and computer programproducts of the present invention advantageously are capable of modelingdemand, supply and associated profitability based on sparse historicaldata or estimates regarding present and future price and quantity of thegood. Also, the present invention is capable of modeling the demand,supply and profitability as a function of the size of the market withinwhich the good is sold over each segment of the period of time, wherethe respective measures are modeled in an improved manner when comparedto conventional techniques. Additionally, the systems, methods andcomputer program products model the demand, supply and associatedprofitability while better accounting for variability in therelationship of the price of the good and the number of units of thegood purchased.

By accounting for variability in the relationship of the price of thegood and the number of units of the good purchased for each timesegment, embodiments of the present invention are capable of modelingdemand, supply and associated profitability while accounting foruncertainty in the price of the good and the number of units of the goodpurchased. Such modeling is advantageous in a number of differentcontexts, such as in the context of commercial transactions. Programsfor the future sale of goods inherently have associated uncertainty,particularly as it relates to the market for the goods, typicallydefined by the number of goods purchased and the price for each unit.According to embodiments of the present invention, then, demand, supplyand associated profitability of a good can be modeled in a manner thatfacilitates deriving an understanding about a future market that isuncertain, particularly when data regarding price and number of units ofthe good purchased are sparse.

According to one aspect of the present invention, a method is providedthat includes defining a plurality of independent component markets fora good. In this regard, each component market can be defined by arespective price sensitivity distribution and market potentialdistribution. The demand and/or supply in the aggregate market can thenbe modeled based upon the price sensitivity distributions and marketpotential distributions of the component markets. More particularly, forexample, demand and/or supply for the good in the component markets canbe modeled based upon respective price sensitivity distributions andmarket potential distributions.

After modeling demand and/or supply for the good in the componentmarkets, those models of demand and/or supply can be combined to therebymodel demand and/or supply for the good in the aggregate market. Inaccordance with a numerical method, for example, the component marketmodels of demand and/or supply can each include a plurality of marketsegments having associated prices per unit. The component market modelscan then be combined by ranking the price per unit of each marketsegment across the component markets in a descending order (or ascendingorder). Then, a cumulative number of units for each different price perunit can be calculated, the cumulative number of units for eachdifferent price per unit equaling the cumulative number of units havinga price per unit no less than the respective price per unit when theprices per unit are ranked in descending order (or the cumulative numberof units having a price per unit less than the respective price per unitwhen the prices per unit are ranked in ascending order). The demandand/or supply for the good in the aggregate market can then be modeledbased upon the different prices per unit and respective cumulativenumber of units.

In accordance with another exemplary method, referred to as themathematical method, a price sensitivity distribution can be for theaggregate market based upon a mean price and an associated standarddeviation for the aggregate market. In such instances, the mean priceand standard deviation may have been calculated based upon a price ofthe good in each of the component markets. The price of the good in eachof the component markets, in turn, may have been determined based uponthe price sensitivity distributions and market potential distributionsof the respective component markets. In addition to the pricesensitivity distribution, a market potential distribution of a number ofunits of the good in the aggregate market can be determined based upon anumber of units of the good in each of the component markets. The numberof goods in each of the component markets may have been determined basedupon the market potential distributions of the respective componentmarkets. Thereafter, the demand and/or supply in the aggregate marketcan be modeled based upon the price sensitivity and market potentialdistributions for the aggregate market.

Systems and computer program products are also provided in accordancewith other aspects of the present invention. Embodiments of the presentinvention therefore are capable of facilitating an understanding aboutdemand and/or supply for a good in an uncertain future market, wheredemand and/or supply can be defined based upon the number of units of agood purchased for a price per unit. Advantageously, the systems,methods and computer program products are capable of modeling thedemand, supply and associated profitability based on sparse historicaldata or estimates regarding price and quantity of the good. Also, byincorporating the unknown size of the market, and by selecting aforecasted market according to the Monte Carlo method, the presentinvention is capable of modeling the demand, supply and, thus theprofitability, as a function of the size of the market within which thegood is sold more adequately than conventional methods of modeling thedemand and supply. Additionally, by including a price sensitivitydistribution, the systems, methods and computer program products modeldemand, supply and associated profitability while better accounting forhow changing the price of the good changes the number of units of thegood purchased. As such, the system, method and computer program productof embodiments of the present invention solve the problems identified byprior techniques and provide additional advantages.

BRIEF DESCRIPTION OF THE DRAWINGS

Having thus described the invention in general terms, reference will nowbe made to the accompanying drawings, which are not necessarily drawn toscale, and wherein:

FIG. 1 is a flowchart illustrating various steps in a method of modelinguncertain future demand over a period of time including a plurality oftime segments, in accordance with one embodiment of the presentinvention;

FIGS. 2 and 3 are flowcharts illustrating various steps in a method ofmodeling demand over a time segment in a non-differentiated market, inaccordance with one embodiment of the present invention;

FIG. 4 is a graphical illustration of future price of a good beingsubject to a contingent activity;

FIG. 5 is a graph of a price sensitivity distribution used duringoperation of the system, method and computer program product of oneembodiment of the present invention;

FIG. 6 is a graph of a market potential distribution used duringoperation of the system, method and computer program product of oneembodiment of the present invention;

FIG. 7 is a schematic illustration of a market penetration distributionfor a forecasted market used during operation of the system, method andcomputer program product of one embodiment of the present invention;

FIG. 8 a is a schematic illustration of a price sensitivity distributionrecast in reverse cumulative format used during operation of the system,method and computer program product for modeling demand according to oneembodiment of the present invention;

FIG. 8 b is a schematic illustration of a price sensitivity distributionrecast in cumulative format used during operation of the system, methodand computer program product for modeling supply according to oneembodiment of the present invention;

FIG. 9 a is a schematic illustration of a demand curve in a forecastedmarket for one time segment in a non-differentiated market, according toone embodiment of the present invention;

FIG. 9 b is a schematic illustration of a supply curve in a forecastedmarket for one segment of a time period including a plurality ofsegments, according to one embodiment of the present invention;

FIGS. 10 and 11 are flowcharts illustrating various steps in a method ofmodeling demand over a time segment in a differentiated market, inaccordance with one embodiment of the present invention;

FIG. 12 a is a schematic illustration of a non-differentiated demandcurve segmented into a plurality of market segments, in accordance withone embodiment of the present invention;

FIG. 12 b is a schematic illustration of a demand curve in a forecastedmarket for one time segment in a differentiated market and in anon-differentiated market, according to one embodiment of the presentinvention;

FIG. 13 a is a schematic illustration of a non-differentiated supplycurve segmented into a plurality of market segments, in accordance withone embodiment of the present invention;

FIG. 13 b is a schematic illustration of a supply curve in a forecastedmarket for one time segment in a differentiated market, according to oneembodiment of the present invention;

FIG. 14 is a flowchart illustrating various steps in a method ofmodeling demand over a time segment in an aggregate market including aplurality of component markets, in accordance with one embodiment of thepresent invention;

FIG. 15 is a schematic illustration of demand curves in three forecastedcomponent markets, as well as in a corresponding aggregate market,according to one embodiment of the present invention;

FIG. 16 is a schematic illustration of a demand curve in a forecastedmarket for three segments of a time period including a plurality ofsegments, according to one embodiment of the present invention;

FIG. 17 is a schematic illustration of a cost curve used duringoperation of the system, method and computer program product of oneaspect of the present invention in the context of a good purchased in anon-differentiated market;

FIG. 18 is a schematic illustration comparing a demand curve with a costcurve, both modeled in accordance with embodiments of the presentinvention;

FIG. 19 is a schematic illustration of a profitability curve accordingto one embodiment of the present invention;

FIG. 20 is a schematic illustration of an optimum number of units of agood sold over a period of time, according to one embodiment of thepresent invention;

FIG. 21 is a schematic illustration of a maximum profit for a good overa period of time, according to one embodiment of the present invention;

FIG. 22 is a schematic illustration of the maximum profit for a goodcompared against the volatility (uncertainty) in the number of units ofthe good sold, according to one embodiment of the present invention; and

FIG. 23 is a schematic block diagram of the system of one embodiment ofthe present invention embodied by a computer.

DETAILED DESCRIPTION OF THE INVENTION

The present invention now will be described more fully with reference tothe accompanying drawings, in which some, but not all embodiments of theinvention are shown. This invention may be embodied in many differentforms and should not be construed as limited to the embodiments setforth; rather, these embodiments are provided so that this disclosurewill be thorough and complete, and will fully convey the scope of theinvention to those skilled in the art. Like numbers refer to likeelements throughout.

I. Modeling Demand and/or Supply for a Good

According to one aspect of the present invention, systems, methods andcomputer program products are provided for modeling demand and/or supplyfor a good. The description will explain modeling demand for goods.Except where indicated, the following description applies equally tomodeling supply for goods. Thus, referring to FIG. 1, modeling uncertainfuture demand for a good generally begins by defining the period oftime, as shown in block 10. The period of time can begin at t=0 andextend to t=T. The period of time can then be divided into a number ofdifferent time segments. In one embodiment, the time period T is definedso that each such time segment can be represented as an integer divisorof T, e.g., t=0, 1, 2, . . . T−1. Thus, for example, the period of timecan be defined as a number of years (i.e., T=30), where the period oftime is divided into a number of one-year time segments (e.g., t=0, 1,2, . . . 29). Each time segment begins at point in time t and ends atpoint in time t+1 (presuming the time segment is an integer divisor ofT), and is defined by the beginning point in time t. Thus, time segmentt=1 extends from point in time t=1 to point in time t=2. Similarly, timesegment t=2 extends from points t=2 to t=3.

Either before, during or after defining the time period, the mean priceand mean market size (number of units) of the good is defined for timesegment t=0, as shown in block 12. The mean price and mean market sizecan be determined in any of a number of different manners such as, forexample, based upon historical data, estimates or the like. Also, afterdefining the time period, a time segment can be selected over which tomodel demand for the good, typically beginning with the time segmentt=1, as shown in block 14.

After selecting a time segment, the uncertain demand over the selectedtime segment is modeled, as shown in block 16. Products can generally becategorized in either a non-differentiated market or a differentiatedmarket. In a non-differentiated market, such as a commodity market,goods are offered at one standard price, like $1.39 per pound or alisted price of $100 M per item. In a differentiated market, the pricesof the goods differ on a sale-by-sale or transaction-by-transactionbasis because of differing perceived values. For example, the storeownermight discount the last three pounds of tomatoes at $1.00 per pound inorder to clear end-of-the-day perishable stock. In another example, thelisted price of $100 M per item could be subjected to privatenegotiations resulting in a better match of the negotiated sale price tothe marginal utility of the item to the consumer. As such, in adifferentiated market, the value of the distinguishing features arerevealed and determined during private negotiations between a supplierand a consumer. Because the negotiated prices remain private, theprocess allows different amounts of goods to be sold at differentprices. For example, wholesale lots of automobiles and aircraft are bothgoods that, due to differing features, can be sold at differing pricesfor differing quantities. Another type of differentiated market is onewhere there are sophisticated pricing systems that exploit smalldifferences among buyer preferences, for example airplane seat, traveland concert seat reservation systems, and department store merchandisepricing coupled with membership discounting.

In a non-differentiated market, all goods are typically sold andpurchased according to a single price for each unit of the good. In adifferentiated market, however, the goods can vary in price. Goods in adifferentiated market are typically sold according to contracts for apredetermined number of units of the good at a predetermined price foreach unit. As such, the present invention provides systems, methods andcomputer program products for modeling demand for goods in anon-differentiated market as well as a differentiated market.

A. Goods in Non-Differentiated Markets

The demand for a good in a non-differentiated market is generally afunction of the price per unit of the good and the size of the market interms of the total number of units of the good in the market, both ofwhich differ depending upon the good. In modeling the demand for somesubsequent time in the future, neither the price of the good nor thesize of the market can be specified as each includes an amount ofuncertainty. Thus, to most accurately model the demand for the good suchthat the uncertainty in the price per unit and/or the size of the marketare captured, the demand is typically modeled based upon a distributionof the possible prices for which the good may be sold, and adistribution of the possible sizes of the market within which the goodmay be sold.

Referring now to FIG. 2 with respect to non-differentiated markets,modeling the uncertain future demand over the selected time segment(e.g., t=1) includes assessing uncertainty in the price per unit of thegood by determining how the price of the good affects whether customerswill purchase the good, or in the case of modeling supply, how the priceof the good affects whether manufacturers will produce the good.Uncertainty in the purchase price of each unit of the good is typicallyexpressed in a price sensitivity distribution (e.g., lognormaldistribution) of a unit purchase of the good at a predetermined price,as shown in block 20. The price sensitivity distribution generallyassigns a probability of a unit purchase to each respective price atwhich consumers would purchase the unit. Advantageously, the pricesensitivity distribution can be developed from sparse data of real orhypothetical consumer purchases of at least one unit of the good atrespective prices per unit developed according to any one of a number ofdifferent methods, such as from a number of historical sales, anexpert's estimation, or a market survey. The distribution shown in FIG.2 can be defined with as few as two points of price data, such as theprice values 10% probability (only 10% of customers will purchase abovea selected price) and 90% probability (90% of customers will purchaseabove a selected price). Additional data points, however, provide betteraccuracy of the price sensitivity distribution estimate.

The price sensitivity distribution for the selected time segment (e.g.,t=1) can be determined in any of a number of different manners, such asin accordance with the method shown in FIG. 3. As illustrated in block32 of FIG. 3, one method of determining a price sensitivity distributionor other value distribution includes defining the growth rate of thegood for the selected time segment. The growth rate can be determinedaccording to any of a number of different techniques, such as accordingto market forecasts. Advantageously, and in contrast to the price pathformulation associated with the Black-Scholes method, the growth ratecan vary from time segment to time segment over the time period. Thus,for example, the growth rate for time segment t=1 can equal 20%, whilethe growth rate for time segment t=2 can equal 20% or, alternatively,any value greater than or less than 20%.

Either during or after defining the growth rate, the uncertainty in themarket including the good can be determined for the selected timesegment (e.g., t=1), as shown in block 34. The uncertainty can bedetermined according to any of a number of different techniques. Theprice sensitivity distribution (value distribution) can then bedetermined based upon the standard deviation in time for the selectedtime segment and the mean market price of the good for the time segment.In one embodiment, for example, the uncertainty is determined based upona statistical analysis of average growth rate or a particular market,versus change in growth rate, resulting in a standard deviationcalculation for uncertainty.

More particularly, in one embodiment for example, the returns can bemodeled from risk values and associated return, or growth values, assuch may be determined by an estimator or the like. Then, assuming atypical linear relationship between risk and return, the risk can bemodeled as a linear function of returns based upon the two risk valuesand associated return values. For example, according to one embodiment,two risk values may comprise 20% and 30%, with associated return valuescomprising 10.0% and 12.5%, respectively. With such values, risk can bemodeled as a linear function of return as follows:Risk(Return)=4×(Return−5)where return and risk are expressed as percentages. For a furtherdescription of modeling risk as a function of returns, see U.S. patentapplication Ser. No. 10/453,395, entitled: Systems, Methods and ComputerProgram Products for Modeling A Monetary Measure for A Good Based UponTechnology Maturity Levels, filed Jun. 3, 2003, the contents of which isincorporated by reference in its entirety. For an example of theuncertainty (risk) associated with various growth rates (returns), assuch may have been determined according to the above, see Table 1.

TABLE 1 Growth Rate Uncertainty 10.0% 20% 12.5% 30% 15.0% 40% 17.5% 50%20.0% 60% 22.5% 70% 25.0% 80% 27.5% 90% 30.0% 100% 

Although a linear relationship between risk and return has been assumedabove, risk and return need not have such a relationship. A linearrelationship between risk and return is approximately reflective of thecapital market relationship of risk and return, embodied in thewell-known Capital Asset Pricing Model (CAPM) theory. In many instances,however, risk and return may not have a linear relationship. Forexample, some goods may have a high projected return with correspondinglow risk when compared to CAPM.

After the growth rate has been defined and the uncertainty has beendetermined for the selected time segment (e.g., t=1) of the time period,the price sensitivity distribution (shown in FIG. 3 as a valuedistribution) can be determined based upon the standard deviation intime for the selected time segment and the mean price of the good forthe time segment, as shown in block 36. The mean price of the good forthe selected time segment can be determined in one embodiment based uponthe mean price of the good for the previous time segment, and the growthrate for the current, selected time segment. For example, the mean priceof the good for the selected time segment can be determined as follows:

$\begin{matrix}{\mu_{t} = {\left( {1 + \frac{{GR}_{t}}{100}} \right) \times \mu_{t - 1}}} & (1)\end{matrix}$In equation (1), μ, represents the mean price of the good for thecurrent selected time segment, μ_(t)−1 represents the mean value of thegood at the immediately preceding time segment, and GR_(t) representsthe growth rate for the current selected time segment, where the growthrate is expressed in terms of a percentage.

Like the mean price of the good for each time segment, the standarddeviation for the selected time segment can be determined in any of anumber of different manners. In one embodiment, for example, thestandard deviation can be determined as follows:σ_(t)=μ_(t)×√{square root over (e ^(σ) ^(avgt) ² ^(xt) −1)}  (2)In equation (2), t represents the current selected time segment, and atrepresents the standard deviation for the current selected time segment.Also in equation (2), σ_(avgt) represents a running average of theuncertainty values from t=1 to the current selected time segment t, andcan be determined, for example, as follows:

$\begin{matrix}{\sigma_{avgt} = \sqrt{\frac{\sum\limits_{i = 1}^{t}\; U_{i}^{2}}{t}}} & (3)\end{matrix}$where U_(i) represents the uncertainty for the ith time segment, andi=1, 2, . . . t. For an example of the values of the growth rate, meanprice of the good, uncertainty and standard deviation for each timesegment in a period of 30 years, where each time segment represents oneyear, see Table 2 below.

TABLE 2 Time Growth Rate Mean Uncertainty Std. Dev. (t) (GR_(t)) (μ_(t))(U_(i)) (σ_(t)) 0 — $500 — — 1 20% $600 60% $395 2 20% $720 60% $739 320% $864 60% $1,205 4 20% $1,037 60% $1,861 5 20% $1,244 60% $2,796 620% $1,493 60% $4,135 7 20% $1,792 60% $6,057 8 20% $2,150 60% $8,816 920% $2,580 60% $12,779 10 20% $3,096 60% $18,471 11 18% $3,653 52%$25,034 12 16% $4,238 44% $32,051 13 14% $4,831 36% $39,026 14 12%$5,411 28% $45,483 15 10% $5,952 20% $51,056 16  8% $6,428 20% $56,26917  6% $6,813 20% $60,866 18  4% $7,086 20% $64,595 19  2% $7,228 20%$67,234 20  0% $7,228 20% $68,608 21  −2%   $7,083 20% $68,609 22  −4%  $6,800 20% $67,209 23  −6%   $6,392 20% $64,466 24  −8%   $5,880 20%$60,518 25 −10%   $5,292 20% $55,577 26 −12%   $4,657 28% $50,880 27−14%   $4,005 36% $46,710 28 −16%   $3,364 44% $43,253 29 −18%   $2,75952% $40,631 30 −20%   $2,207 60% $38,942

Future demand can be subject to a contingent activity, or event, whichcan impact the future demand (mean and uncertainty values) forsubsequent time segments. For example, price (upon which demand isbased) over a time segment can be subject to a contingent event, whichreduces the price of the good, as shown in FIG. 4 at time t=3. Byreducing the price, the mean price of the good (i.e., μ_(t)−1) may belowered (or raised) in the determination of the mean value over asubsequent time segment (i.e., μ_(t)). As will also be appreciated, thecontingent activity can itself be represented as a probabilitydistribution. For example, the contingent activity comprising a suddenchange in the price of oil, or an unforeseen catastrophe can berepresented by a price of the good if the contingent activity comes tofruition, and an associated probability of the contingent activitycoming to fruition. Thus, as the mean value and standard deviation aredetermined, any contingent activities to which the price of the good forthe selected time segment are subject can be accounted for to adjust thegrowth rate, uncertainty, mean value and/or standard deviationaccordingly. By linking each time segment to the outcome of the priortime segment, embodiments of the present invention can advantageouslyprovide the flexibility to incorporate contingent activities orendeavors or decisions that may occur at the transition between timesegments.

After determining the mean value of the good and standard deviation overthe selected time, the price sensitivity distribution can be determinedfor the selected time segment by defining the respective pricesensitivity distribution according to the respective mean value of thegood and standard deviation. The price sensitivity distribution can beexpressed according to any of a number of different probabilitydistribution types such as normal, triangular or uniform. But becausethe economy typically functions in a lognormal fashion, in a typicalembodiment the price sensitivity distribution is expressed as alognormal probability distribution. FIG. 5 illustrates an exemplaryprice sensitivity distribution defined for a selected time segment(e.g., t=1).

Again referring to FIG. 2, a market potential distribution can similarlybe determined before, after or during determination of the pricesensitivity distribution, irrespective of exactly how the pricesensitivity distribution is determined, as shown in block 22. Inaddition to factoring uncertainty in the price of the good into thedemand for the good over the selected time segment, the demand canadvantageously be modeled as a function of the size of the market withinwhich the good is purchased to thereby account for uncertainty in thesize of the market. Uncertainty in the size of the market is typicallyrepresented as a market potential that refers to the total number ofunits of the good consumers will purchase presuming all consumerrequirements are met, including price. The market potential is typicallyexpressed as a distribution of consumers purchasing a predeterminednumber of units of the good. The market potential distribution generallyassigns a probability to each respective number of units of the goodconsumers will purchase presuming all consumer requirements are met.

The market potential distribution for the selected time segment (e.g.,t=1) can be determined in any of a number of different manners but, inone typical embodiment, the market potential is determined in a mannersimilar to that of the price sensitivity distribution (see FIG. 3). Moreparticularly, the growth rate and uncertainty in the market determinedfor the selected time segment can be determined in the same manner asthat explained above (see blocks 32 and 34), and can be the same ordifferent from that determined for the price sensitivity distribution.The market potential distribution (value distribution) can then bedetermined based upon the standard deviation in time for the selectedtime segment and the mean market size (number of units) of the good forthe time segment. In accordance with equation (1) above, for example,the mean market size (i.e., μ_(t)) for the selected time segment isdetermined based upon the mean market size for the previous time segment(i.e., μ_(t−1)), and the growth rate for the current, selected timesegment. Likewise, in accordance with equations (2) and (3) above, forexample, the standard deviation for the selected time segment can bedetermined based upon the mean market size for the selected time segmentand a running average (i.e., σ_(avgt)) of the uncertainty values fromt=1 to the current selected time segment. The market potentialdistribution can then be determined based upon the standard deviation intime for the selected time segment and the mean market size for the timesegment (see block 36).

Advantageously, the market potential distribution can also be developedfrom sparse data from any one of a number of different sources, such asmarket studies or a myriad of other factors as known to those skilled inthe art. The market potential distribution can be expressed according toany of a number of different probability distribution types such asnormal, triangular or uniform but, like the market sensitivitydistribution, the market potential distribution is typically expressedas a lognormal probability distribution. For example, FIG. 6 illustratesan exemplary market potential distribution defined for a selected timesegment (e.g., t=1).

The demand for the good is modeled as a function of the size of themarket within which the good is sold. Thus, to model the demand for thegood for the selected time segment (e.g., t=1), a forecasted market of apredefined total number of units of the good is selected from the marketpotential distribution for the selected time segment. Advantageously,the number of units in the forecasted market is selected according to amethod for randomly selecting a predefined number of units of the good,such as the Monte Carlo method. As known to those skilled in the art,the Monte Carlo method is a method of randomly generating values foruncertain variables to simulate a model. The Monte Carlo method isapplied to the market potential distribution to select the predefinednumber of units of the good in the forecasted market, as shown in block24 of FIG. 2.

As manufacturers will typically not be capable of capturing all (i.e.,100%) of the market for a good, demand for the good can be modeled toaccount for different percentages of the market that a manufacturer maycapture. Therefore, from the forecasted market for the selected timesegment (e.g., t=1), a market penetration distribution for the selectedtime segment can be determined based upon different numbers of unitsthat represent corresponding percentages of the forecasted market, asshown in block 26. For example, as shown in FIG. 7, in a market size of700 units of the good, a sale of 350 units would be associated with amarket penetration of 50%. In an alternative market penetrationdistribution, represented as a dotted line in FIG. 7, in a market sizeof 700 units of the good, a sale of 200 units would be associated with amarket penetration of 50%. As will be appreciated, then, the marketpenetration may or may not directly correspond to the ratio of unitssold/units available. In this regard, although market penetration mayinitially correspond to the ratio of units sold/units available, anumber of different factors may cause the values to deviate. Forexample, volume discounting may curve the market penetrationdistribution in a non-linear manner, such as in the case represented bythe dotted line in FIG. 7. By comparison, the case represented by thestraight line may represent a risk neutral market without volumediscounting, such as a true commodity market. Increasing curvature ofthe straight line, then, may imply a risk-adverse market where largerunit purchases are price discounted to account for the consumer'sdecreasing utility of additional purchased units. Thus, the dotted,curved line in FIG. 7 may represent a negative correlation between priceand units sold in a contract (differentiated market).

Once the market penetration distribution has been determined, the demandfor the selected time segment can be modeled based upon the pricesensitivity distribution and the market penetration distribution for theselected time segment. To combine the price sensitivity distribution andthe market penetration distribution, the price sensitivity distributionis typically first recast in reverse cumulative format, as shown in FIG.8 a. (see FIG. 2, block 28). As will be apparent, a reverse cumulativedistribution depicts the number, proportion or percentage of valuesgreater than or equal to a given value. The reverse cumulative of theprice sensitivity distribution represents the distribution of a unitpurchase of the good for at least a predetermined price, i.e., at orabove a predetermined price.

Similarly, when modeling supply for the selected time segment (e.g.,t=1), to combine the price sensitivity distribution and the marketpenetration distribution, the price sensitivity distribution istypically first recast in cumulative format, as shown in FIG. 8 b. Aswill be apparent, a cumulative distribution depicts the number,proportion or percentage of values less than or equal to a given value.The cumulative of the price sensitivity distribution represents thedistribution of a unit manufactured when the market price for the goodis at least a predetermined price, i.e., at or above a predeterminedprice.

Once the price sensitivity distribution has been recast, the demand forthe good in the forecasted market for the selected time segment (e.g.,t=1) can be modeled based upon the reverse cumulative of the pricesensitivity distribution and the market penetration distribution, asshown in block 30 of FIG. 2. For the forecasted market, the demandrepresents the number of units consumers will purchase for at least agiven price, i.e., at or above a given price. To model the demand, eachprobability percent of the reverse cumulative of the price sensitivitydistribution is associated with a corresponding percentage of theforecasted market from the market penetration distribution. Thus, eachof a plurality of different numbers of units of the good from the marketpenetration distribution are linked to a minimum price per unit from thereverse cumulative price sensitivity distribution having a probabilitypercent equal to the market penetration percent for the respectivenumber of units. As such, the demand model can be thought of as aplurality of different numbers of units sold in the forecasted market,each number of units having a corresponding minimum price at whichconsumers will purchase the respective number of units. For example, anumber of goods totaling 700 and having a market penetration of 100% islinked to a price per unit of approximately $77 million dollars having aprobability percent of 100%. Thus, according to the demand model, 700units of the good will sell for at least $77 million dollars. The demandmodel can be represented in any one of a number of manners but, in oneembodiment, the demand model is represented as a demand curve byplotting different numbers of units sold in the forecasted market versusthe minimum price consumers will pay per unit for the good, as shown inFIG. 9 a.

Similar to modeling demand, the supply for the product in the forecastedmarket for the selected time segment (e.g., t=1) can be modeled basedupon the cumulative of the price sensitivity distribution and the marketpenetration distribution. For the forecasted market, then, the supplyrepresents the number of units manufacturers will produce when themarket price for the good is at least a given price, i.e., at or above agiven price. To model the supply, each probability percent of thecumulative of the price sensitivity distribution is associated with acorresponding percentage of the forecasted market from the marketpenetration distribution. Thus, each of a plurality of different numbersof units of the good from the market penetration distribution are linkedto a maximum price per unit from the cumulative price sensitivitydistribution having a probability percent equal to the marketpenetration percent for the respective number of units. As such, thesupply model can be thought of as a plurality of different numbers ofunits produced in the forecasted market, each number of units having acorresponding maximum market price. Like the demand model, the supplymodel can be represented in any one of a number of manners. In oneembodiment, for example, the supply model is represented as a supplycurve by plotting different numbers of units produced in the forecastedmarket versus the maximum market price of the good, as shown in FIG. 9b.

As indicated above, the demand for the good for the selected timesegment (e.g., t=1) is based upon the reverse cumulative of the pricesensitivity distribution and the market penetration distribution for theselected time segment, and the supply for the good is based upon thecumulative of the price sensitivity distribution and the marketdistribution for the selected time segment. The steps in determining thereverse cumulative (or cumulative) of the price sensitivity distributionand the market penetration distribution can be accomplished in any orderrelative to one another without departing from the spirit and scope ofthe present invention. For example, the price sensitivity distributioncan be rewritten in reverse cumulative format before any or all of thesteps in determining the market penetration distribution from the marketpotential distribution.

B. Goods in Differentiated Markets

Just as in the case of non-differentiated markets, to most accuratelymodel the demand and/or supply for the good in an uncertain,differentiated market over a period of time, the demand is typicallymodeled based upon a distribution of the possible prices for which thegood may be sold, and a distribution of the possible sizes of the marketwithin which the good may be sold and/or produced. Thus, the demandand/or supply for a good in a differentiated market over a period oftime can be modeled based upon a price sensitivity distribution and amarket potential distribution for each time segment, such as thoseexplained above.

As previously stated, however, non-differentiated markets differ fromdifferentiated markets in that goods in non-differentiated markets areall sold and purchased for a uniform price, as opposed to differingprices based on individual units. In a differentiated market, the goodsare sold according to contracts that each specify a predetermined numberof units of the good at a predetermined price for each unit. Thus, notonly does the price of the good change with the size of the market, butthe price changes with each contract within the size of the market. Assuch, for differentiated markets, modeling the demand for the good mayfurther include assessing the uncertainty in the number of contracts inthe market, as well as uncertainty in the predetermined number of unitsof the good in each contract and the predetermined price per unit atwhich each unit in each contract is purchased. For more information onone such method for modeling demand and/or supply, as well aspatentability, for a good in a forecasted, differentiated market, seeU.S. patent application Ser. No. 10/453,727, entitled: Systems, Methodsand Computer Program Products for Modeling Demand, Supply and AssociatedProfitability of a Good, both filed on Jun. 3, 2003.

Referring now to FIG. 10, in another method for modeling demand in adifferentiated market, demand in a differentiated market is estimatedfrom demand in a non-differentiated market. Briefly, in accordance withthis embodiment of the present invention, demand in a differentiatedmarket is modeled by first modeling demand in a non-differentiatedmarket, as shown in block 38. Whereas demand in the non-differentiatedmarket can be modeled in any of a number of different manners, in oneembodiment demand in the non-differentiated market is modeled in themanner explained above with reference to FIGS. 2-9. Thereafter, thenon-differentiated demand model is integrated over the forecasted marketto model or otherwise estimate demand for the good in a correspondingdifferentiated market.

Whereas the non-differentiated demand model can be integrated in any ofa number of different manners to model demand in a correspondingdifferentiated market, one method of integrating a non-differentiateddemand model will now be described with reference to FIG. 11. As shownin block 42 of FIG. 11, one method for integrating a non-differentiateddemand model includes segmenting the forecasted market into a pluralityof market segments. The forecasted market can begin with unit u=0 andextend to u=U, where U represents the size of the forecasted market. Theforecasted market can then be segmented into a number of differentmarket segments. In one embodiment, the forecasted market U is definedsuch that each market segment can be represented as a percentage of U,i.e., u=1% U, 2% U, . . . , 100% U. Thus, for example, the forecastedmarket can be defined as a number of units of the good (e.g., U=700),where the forecasted market is divided into one hundred one-percentmarket segments.

Each market segment begins with unit u−1% U and ends with unit u, and isdefined by the ending unit U. Thus, market segment u=1% U extends fromunit u=0 to unit u=1% U (e.g., 7 for U=700). Market segment u=2% Uextends from unit u=1% U to unit u=2% U (e.g., 14 for U=700). Similarly,market segment u=3% U extends from units u=2% U to u=3% U (e.g., 21 forU=700). The market segments then continue until market segment u=100% U,which extends from units u=99% U (e.g., 693 for U=700) to u=100% U(e.g., 700 for U=700). For an example of the segmentation of the marketof the non-differentiated demand model of FIG. 9 a, see FIG. 12 a.

After segmenting the forecasted market into a plurality of marketsegments, a market segment can be selected, typically beginning with themarket segment u=1% U, as shown in block 44. After selecting a marketsegment, the price per unit of the good over the selected market segmentis calculated. As previously indicated, the demand for the good in theforecasted market represents the number of units consumers may purchasefor at least a given price. Thus, the price per unit of the selectedmarket segment can be calculated by calculating the average thenon-differentiated market price per unit of the good for the marketsegments up to, and including, the selected market segment, andassociating the average with the selected market segment, as shown inblocks 46 and 48. Thus, for the first market segment u=1% U, the averagenon-differentiated market price per unit can be calculated from thenon-differentiated demand model as the non-differentiated market priceper unit for u=1% U units (e.g., 7 units).

The price per unit of the good can be calculated for each market segment(e.g., u=1% U, 2% U, . . . 100% U) of the forecasted market, as shown inblock 50, and again in blocks 44, 46 and 48. For each market segment ofthe forecasted market, the associated price per unit can be calculatedby averaging the non-differentiated market price per unit of the goodfor the market segments up to, and including, the respective marketsegment. For market segment u=2% U, then, the average non-differentiatedmarket price per unit can be calculated by summing thenon-differentiated market price per unit for u=1% U units and u=2% Uunits (e.g., 14), and dividing the sum by two. For market segment u=3%U, the average non-differentiated market price per unit can becalculated by summing the non-differentiated market price per unit foru=1% U units, u=2% U units and u=3% U units (e.g., 21), and dividing thesum by three. Finally, for market segment u=100% U, the averagenon-differentiated market price per unit can be calculated by summingthe non-differentiated market price per unit for u=1% U units throughu=100% U units (e.g., 700), and dividing the sum by one hundred.

After calculating an associated price per unit for each market segmentin the forecasted market, demand for the good in the differentiatedmarket can be modeled or otherwise estimated based upon the units u thatdefine the market segments and the respective, associated prices perunit, as shown in block 52. As such, the differentiated demand model canbe thought of as a plurality of different numbers of units sold insegments of the forecasted market, each number of units having acorresponding minimum price at which consumers will purchase therespective number of units. Similar to the non-differentiated demandmodel, the differentiated demand model can be represented in any one ofa number of manners but, in one embodiment, the differentiated demandmodel is represented as a demand curve by plotting the numbers of unitssold in the forecasted market for the different market segments versusthe minimum price consumers will pay per unit for the good, as shown inFIG. 12 b against a corresponding non-differentiated demand model.

Similar to modeling demand, the supply for the product in a forecasted,differentiated market for the selected time segment (e.g., t=1) can bemodeled in a number of different manners, including that described inU.S. patent application Ser. No. 10/453,727. Alternatively, in a mannersimilar to that of modeling demand explained more particularly above,supply in a differentiated market can be modeled or otherwise estimatedbased upon a corresponding non-differentiated supply model. To model thesupply, non-differentiated supply can be modeled, such as in the mannerexplained above. Thereafter, differentiated supply can be modeled byintegrating the non-differentiated supply model. More particularly,differentiated supply can be modeled by segmenting the forecasted marketinto a plurality of segments, as shown, for example, in FIG. 13 a forthe non-differentiated supply model of FIG. 9 b. For each segment, then,an associated price per unit can be calculated by averaging thenon-differentiated market price per unit of the good for the marketincluding, and after, the respective market segment. Thus, the supplymodel can be thought of as the numbers of units produced in theforecasted market for each of a plurality of market segments, eachmarket segment having a corresponding maximum market price. Like thedemand model, the supply model can be represented in any one of a numberof manners. In one embodiment, for example, the supply model isrepresented as a supply curve by plotting the numbers of units producedin the forecasted market for the different market segments versus themaximum market price of the good, as shown in FIG. 13 b against acorresponding non-differentiated supply model.

Just as in the case of modeling demand/supply in a non-differentiatedmarket, the steps in modeling demand/supply in a differentiated marketcan be accomplished in any of a number of different orders relative toone another, including the order explained above, without departing fromthe spirit and scope of the present invention. For example, the marketsegments can be selected beginning with the last market segment (e.g.,u=100% U), and proceed through to the first market segment (e.g., u=1%U). It should further be understood that demand/supply in thedifferentiated market need not be modeled across the entire forecastedmarket. Differentiated demand/supply can be modeled from the firstmarket segment through a portion of the forecasted market (e.g., u=50%U), from the last market segment through a portion of the forecastedmarket, or for an intermediate portion of the forecasted market (e.g.,from u=20% U through u=80% U).

C. Goods in Aggregate Markets

Various markets for goods are actually aggregate markets formed of aplurality of independent markets that at least partially converge withone another. In the travel industry, for example, an aggregate travelermarket may be formed when travelers from several connecting citiesconverge on a city-pair travel. More particularly, for example,travelers may have different origin and destination cities, but convergeon a particular city-pair to complete their journey. Thus, a city-pair(A to B) market may comprise an aggregate market of up to fourindependent traveler route markets: “A to B,” “behind A to B.” “A tobeyond B,” and “behind A to beyond B.” In another exemplary industry,the automotive industry, aggregate automobile markets for differenttypes of automobiles, such as trucks, sedans, sport utility vehicles(SUVs) and the like, where the aggregate markets may be formed fromcomponent markets for different characteristics of the respective typesof automobiles, such as for different makes, models or the like. Moreparticularly, for example, an aggregate SUV market may be formed ofcomponent SUV markets, where all of the component markets generallyinclude SUVs, but are distinct from one another in characteristics ofthe SUVs in the respective component market (e.g., size, performance,price, etc.). Thus a SUV market may comprise an aggregate of smallercomponent SUV markets, such as a compact SUV market, mid-size SUVmarket, full-size SUV market, luxury SUV market and/or hybrid SUVmarket.

As will also be appreciated, in instances of an aggregate marketincluding a plurality of individual markets, one or more of the marketsmay influence, or be correlated with, one or more of the other markets,thereby causing distortions in the aggregate market. In the travelindustry, for example, each origin-destination market may have its ownprice (e.g., fare) and number of units of a good (e.g., travel tickets)relationship depending upon underlying economic dynamics. Travelers maypay differing prices for units of a good with differing origin anddestination cities, but which include a common city-pair. However,because a number of travel industries (e.g., airline industry) apportionrevenues to the distance the traveler travels (e.g., revenue seatmiles), revenues from different travelers for the same city-pair maydiffer. Thus, demand in the aggregate market may exhibit price-unitrelationship distortions as a result of differing economic dynamics ofthe underlying contributing markets. These distortions may beindications of market place inefficiencies. Conventionally, however,these distortions are typically not sufficiently reflected in modelingdemand for the good in the aggregate market. Thus, in instances of agood in an aggregate market, embodiments of the present invention permitindividually modeling demand/supply for the good in the componentmarkets that form the aggregate market, and then aggregating theindividual models to form an aggregate market model.

One method for modeling demand/supply for a good in an aggregate marketwill now be described with reference to FIG. 14. As shown and describedwith respect to FIG. 14, demand is modeled for a good in an aggregate,differentiated market. It should be understood, however, that supply canbe similarly modeled for a good in an aggregate, differentiated marketwithout departing from the spirit and scope of the present invention.Further, it should be understood that demand and/or supply can equallybe modeled for a good in an aggregate, non-differentiated market.

As shown in block 54 of FIG. 14, a method of modeling demand in anaggregate market includes defining the component markets forming theaggregate market. Each component market can be defined in any of anumber of different manners. In one embodiment, for example, eachcomponent market is defined by a price sensitivity distribution and, ifso desired, a market potential distribution, where the distributions maybe determined in a manner such as that explained above. Then, afterdefining the component markets, demand for the good in each of thecomponent markets is modeled as shown in block 56. In the case ofdifferentiated markets, for example, demand for the good in each of thecomponent markets can be modeled in the manner explained above withrespect to FIGS. 10 and 11.

After modeling demand for the good in each of the component markets, thecomponent-market demand models are combined to model demand for the goodin the aggregate market, as shown in block 58. The component-marketdemand models can be combined in a number of different manners. Onetechnique, referred to as the numerical method, models demand in theaggregate market utilizing the market segments and prices per unit ofthe good associated with those market segments for the component markets(calculated for the market segments during modeling of the componentmarkets). In another technique, referred to as the mathematical method,demand in the aggregate market is modeled utilizing the market segmentsof the component markets and the distribution(s) defining the componentmarkets.

More particularly, modeling demand in the aggregate market in accordancewith the numerical method includes ranking the price per unit of eachmarket segment across all of the component markets, such as in anascending order from the lowest price per unit up, or in a descendingorder from the highest price per unit down. A cumulative number of unitsfor each different price per unit can then be calculated. In the case ofranking the price per unit in descending order, the cumulative number ofunits for each price can equal the cumulative number units sold for aprice per unit equal to or greater than the respective price across allmarket segments of all of the component markets. Alternatively, in thecase of ranking the price per unit in ascending order, the cumulativenumber of units for each price can equal the cumulative number unitssold for a price per unit less than the respective price across allmarket segments of all of the component markets. More particularly, forexample, when ranking the price per unit in descending order, thecumulative number of units associated with the highest price per unitwould equal the number of units in each market segment having thehighest price per unit. Then, the cumulative number of units associatedwith the second highest price per unit would equal the number of unitsin each market segment having the second highest price per unit plus thenumber of units in each market segment having the highest price perunit.

Continuing the numerical method, with each different price per unit andthe associated cumulative number of units, demand for the good in theaggregate market can be modeled based upon the price per unit of each ofthe segments and the cumulative number of units sold for a price perunit equal to or greater than the respective price per unit. As before,the aggregate market demand model can be thought of as a plurality ofdifferent numbers of units sold in the forecasted, aggregate market,each number of units having a corresponding minimum price at whichconsumers will purchase the respective number of units. For examples ofthe demand of three component markets modeled relative to one anotherand relative to the corresponding aggregate market, see FIG. 15.

The mathematical method of combining the component-market demand modelsto model demand in the aggregate market provides a nearly equivalent,but typically computationally more efficient, implementation than thenumerical method to calculate aggregation of component markets. Inaccordance with one embodiment, modeling demand in the aggregate marketin accordance with the mathematical method includes calculating a meanprice of the good and an associated standard deviation for the aggregatemarket. The mean and associated standard deviation for the aggregatemarket can be calculated in any of a number of different manners.Consider, for example, the case of differentiated markets, when demandfor the good in each of the component markets is modeled in the mannerexplained above with respect to FIGS. 10 and 11. In such a case, themean can be calculated by first calculating an average price of the goodin each of the component markets, such as by averaging the price perunit of the good for each market segment (e.g., u=1% U, 2% U, . . . 100%U) of the respective component markets. The average price for eachcomponent market can then be weighted by multiplying the average priceby the fraction of the number of units of the good in the componentmarket to the number of units in the aggregate market. Thereafter, themean can be calculated by summing the weighted average prices for thecomponent markets.

Similar to the technique for calculating the mean, the associatedstandard deviation for the aggregate market can be calculated based uponweighted contributions of the component markets to the overall aggregatemarket. The calculation of the standard deviation can be similar tostandard variance equations. In this regard, for component markets k=1,. . . n, the total number of units in the aggregate market, U, can becalculated by summing the number of units in the component markets,U_(k). For the market segments (e.g., u_(k)=1% U_(k), 2% U_(k), . . .100% U_(k)) of the respective component markets, first and second sumvalues can be calculated as follows:

$\begin{matrix}{{{Sum}\; 1} = {\sum\limits_{{u = {1\%\mspace{14mu} U}},{k = 1}}^{{100\%\mspace{14mu} U},n}\;{u_{k} \times {\sum\limits_{u = {1\%\mspace{11mu} U}}^{100\%\mspace{14mu} U}\;{Price}_{u_{k}}^{2}}}}} & (4) \\{{{Sum}\; 2} = {\sum\limits_{{u = {1\%\mspace{14mu} U}},{k = 1}}^{{100\%\mspace{14mu} U},n}\;{u_{k} \times {\sum\limits_{u = {1\%\mspace{11mu} U}}^{100\%\mspace{14mu} U}\;{Price}_{u_{k}}}}}} & (5)\end{matrix}$where Price_(u) _(k) represents the price per unit of the good for therespective market segment of the respective component market.Thereafter, the standard deviation for the aggregate market can becalculated in accordance with the following equation (6):

$\begin{matrix}{{MultiMarketStdDev} = \sqrt{\frac{\left( {U \times {Sum}\; 1} \right) - {{Sum}\; 2^{2}}}{U^{2} - U}}} & (6)\end{matrix}$

After determining the mean value of the good and standard deviation overthe selected time, a price sensitivity distribution of a unit purchaseof the good in the aggregate market can be determined for the selectedtime segment by defining the respective price sensitivity distributionaccording to the respective mean value of the good and standarddeviation, such as in the same manner explained above and in theaforementioned '727 application (see FIG. 5).

In addition to a price sensitivity distribution, a market penetrationfor the aggregate market can be determined from the aggregate number ofunits of the good, U. More particularly, for example, a marketpenetration for the aggregate market can be determined based upon thedifferent numbers of units that represent corresponding percentages ofthe forecasted market, as also explained above and in the '727application (see FIG. 7). Then, once the price sensitivity and marketpenetration distributions have been determined, the demand for the goodin the aggregate market can be modeled based upon the price sensitivitydistribution and the market penetration distribution for the selectedtime segment. To combine the price sensitivity distribution and themarket penetration distribution, the price sensitivity distribution canbe recast in reverse cumulative format (see FIG. 8 a). Demand for thegood in the aggregate market can then be modeled based upon the reversecumulative of the price sensitivity distribution and the marketpenetration distribution, such as in the same manner explained above andin the '727 application (see FIG. 9 a).

Again referring to FIG. 1, irrespective of whether demand in theaggregate market is modeled in accordance with the numerical method orthe mathematical method, the demand for the good in the market can bemodeled for each time segment (e.g., t=1, 2, . . . T) of the time periodT, as shown in block 18, and again in blocks 14 and 16. Unless otherwiseindicated, the “market” described below may comprise anon-differentiated or differentiated market, which may represent asingle market, component market or aggregate market. For each timesegment of the time period in a non-differentiated market, for example,a price sensitivity distribution and market potential distribution canbe determined (see blocks 20 and 22). Also for each time segment, aforecasted market size can be selected, with a market penetrationdistribution determined based upon the forecasted market (see blocks 24and 26). The price sensitivity distribution can be rewritten into areverse cumulative distribution (see block 28), which can thereafter beused with the market penetration distribution to model demand for therespective time segment. Thus, each time segment can include a differentprice sensitivity distribution, market potential distribution,forecasted market, market penetration distribution and reversecumulative price sensitivity distribution, thus resulting in a differentmodel of the demand for the good. For example, for a time period ofthirty years (T=30) with one-year segments, the good can have anassociated demand model for each year, which can remain the same ordiffer from one year to the next. The demand model for the differentsegments can be represented in any one of a number of manners but, inone embodiment, the demand models are represented as demand curves byplotting different numbers of units sold in the forecasted market foreach segment versus the minimum price consumers will pay per unit forthe good, as shown with respect to three segments (i.e., years 1, 10 and19) in FIG. 16.

As described below, modeling the demand for the good can be used with acost model to model profitability for the good in the forecasted marketfor each time segment. In turn, the profitability model can be used todetermine conclusions regarding the good over the period of time, suchas the optimum price per unit and the number of units sold for each timesegment. The conclusions for the segments of the time period can then beused, such as by the manufacturer, to facilitate an understanding of howuncertainty in the price of the good and number of units in the marketaffect demand for the good over time. With such an understanding, themanufacturer can be in a better position to select a price at which tosell each unit of the good, as well as a number of units of the good toproduce.

II. Modeling the Profitability of a Good

By utilizing the demand for the good, modeled over the time segments ofthe time period according to embodiments of the present invention, theprofitability of the good over the time segments of the time period canbe modeled thereby facilitating an understanding of how uncertainty indemand for the good, as well as uncertainty in cost of producing thegood, can affect profitability over time. Just as the demand modeldiffers depending on whether the goods are in a non-differentiatedmarket or a differentiated market, the profitability of the good alsodiffers depending on the type of market. As such, the present inventionprovides systems, methods and computer program products for modeling theprofitability of a good over time in both non-differentiated markets aswell as differentiated markets.

A. Goods in Non-Differentiated Markets

Modeling the profitability of a good over segments of a time period in anon-differentiated market generally includes modeling the demand for thegood over those segments, such as according to embodiments of thepresent invention as described above with reference to FIGS. 1-9. Alongwith modeling the demand for the good, the cost of producing the good isalso modeled over the segments of the time period. The cost model foreach time segment can be based on the average cost per unit to producethe good and the number of units produced, or sold. The cost model for atime segment accounts for uncertainty in the size of the market, just asdoes the demand model for that time segment. Further, whereas the costof producing the good can be modeled in any one of a number of manners,the cost preferably considers the effect of the number of unitsproduced, or sold, on the cost to produce each unit of the good. Costsassociated with producing a good in many markets tend to decline as themanufacturer gains experience with that production.

Whereas one might expect the cost of producing each unit of the good toremain constant, the cost to produce each unit of the good is typicallymore than the expected cost of producing each unit for the first unitsproduced. And as the number of units produced increases, themanufacturer typically gains experience that drives the cost to produceeach unit down to and below the expected cost, and thereafter eventuallyleveling to an optimum cost of producing each unit. The change in thecost to produce each unit can generally be considered to be attributableto a “learning curve” experienced by the manufacturer in manufacturingthe good. A cost model accounting for a learning curve can berepresented in any one of a number of different manners but, in oneembodiment, the cost model is represented as a reverse cumulative costcurve by plotting the different costs per unit versus the cumulativenumber of units produced for the respective cost per unit, as shown inFIG. 17. As an example of one method by which the cost to produce eachunit of a good in a non-differentiated market can be modeled, see U.S.patent application Ser. No. 10/453,779, entitled: Systems, Methods andComputer Program Products for Determining A Learning Curve Value andModeling Associated Profitability and Costs of A Good, filed Jun. 3,2003, the contents of which are hereby incorporated by reference in itsentirety.

For a given time segment t of the time period T, once the demand andcost have been modeled for a forecasted market, the profitability forthe good in the forecasted market for the respective time segment can bemodeled. The profitability for a time segment can be represented as theresult of subtracting the cost per unit from the price per unit andmultiplying the difference by the number of units sold for thecorresponding fraction of the forecasted market. Graphically, as shownin FIG. 18 with respect to a given time segment, by simultaneouslyplotting the demand curve and the cost curve for the forecasted market,the profitability for the respective time segment can be seen asdirectly related to the distance between the two curves. Like the demandmodel and the cost model, the profitability model for the respectivetime segment can be represented in any one of a number of differentmanners. In one embodiment, shown in FIG. 19, the profitability modelfor a given time segment can be represented as a profitability curve byplotting the number of units that must be sold to achieve at least agiven profit.

From the profitability model, as well as the demand and cost models,conclusions regarding the forecasted market of the respective timesegment can be drawn from collectively modeling the demand, cost andprofitability for the forecasted market of the respective time segment.For example, the maximum profit for the good in the forecasted market ofthe respective time segment can be seen as the point where the priceexceeds the cost by the greatest amount. By determining the maximumprofit, the optimum price for each unit of the good and the optimumnumber of units sold in the forecasted market (i.e., fraction of thenumber of goods in the market), as well as the corresponding costassociated with the optimum price and number of units sold, in theforecasted market of the respective time segment can be determined.Additionally, or alternatively, other conclusions respective of themaximum profit, the optimum price, number of units and cost can bedetermined for the respective time segment. For example, the maximumprofit margin for the forecasted market of the respective time segmentcan be determined by dividing the difference between the optimum priceand associated cost by the optimum price, and thereafter recorded.Further, the price per unit and number of units at which the forecastedmarket clears can be determined from the point where the profitabilityis zero (or the point where the demand model intersects the cost model).

The profitability for the good in a forecasted market can similarly bemodeled for each of the time segments t of the time period T, withconclusions drawn from the respective demand, cost and profitabilitymodels for the respective time segments. Those conclusions can then beplotted to develop or otherwise create a business case for the good overtime. For example, the business case can receive the optimum number ofunits for each time segment, and plot the optimum number of units overthe time period, as shown in FIG. 20. Similarly, for example, thebusiness case can receive the maximum forecasted profit (e.g., grossprofit) for each time segment, and plot the maximum profit over the timeperiod, as shown in FIG. 21. In another example, the business case canreceive the maximum forecasted profit for each time segment, and plotthe maximum profit against the volatility (uncertainty) in the number ofunits of the good sold (see block 22 of FIG. 2 with respect todetermining the market potential distribution), as shown in FIG. 22.From the illustrated scatter plot, then, a best fit curve can be formedfrom the points of maximum profit and associated uncertainty in thenumber of units of the good to illustrate the consistency, or lackthereof, in profitability of the good in an uncertain market.

B. Goods in Differentiated Markets

In differentiated markets, modeling the profitability can proceed in amanner similar to that explained above with respect to modeling theprofitability in non-differentiated markets. The demand for the good andcost of producing the good for each time segment can be modeled in amanner similar to that explained above and in U.S. patent applicationSer. No. 10/453,727. Profitability in the differentiated market for eachtime segment can then be represented in a manner similar to thenon-differentiated market. Further, just as in the case with goods innon-differentiated markets, in differentiated markets conclusionsregarding the forecasted market for each time segment can be drawn fromcollectively modeling the demand, cost (or lowest cost value) andprofitability for the forecasted market in the respective time segments.

In the case of both non-differentiated markets and differentiatedmarkets, for certain quantities of units sold in certain time segments,the profitability model actually demonstrates a negative profitability,or a loss for sales of the good, as shown in FIG. 19. Thus, it isoftentimes desirable to determine whether the profitability of the goodis positive before exercising a contingent claim, such as whether toinitiate or continue the project. Alternatively, it is desirable todetermine whether the profitability of the good is above a predeterminedthreshold before exercising the contingent claim. Contingent claimsoftentimes come in the form of a call in which the manufacturer has anoption to invest an amount of money, or additional amounts of money, inorder to start producing or continue producing the good. As such, if theinitial stages of the production and sale of the good have provedunsuccessful and/or if the future prospects for the profitability of thegood appear bleak, the manufacturer will likely decline to invest themoney, or additional money, and thereby forego exercise of the call andwill therefore decline to produce the good or terminate production ofthe good. Alternatively, if the initial stages of the production andsale of the good have been successful and/or if the prospects of theprofitability of the good are bright, the manufacturer will likely makethe necessary investment in order to begin or continue production of thegood.

Regardless of the type of contingent claim, it is desirable to determinethe value of a good and, in particular, the contingent claim at thepresent time. By determining the value of the contingent claim, themanufacturer can avoid overpaying for production of the good as a resultof an overvaluation of the contingent claim. Conversely, themanufacturer can identify goods in which the value of the contingentclaim has been undervalued and can give strong consideration toinvesting in the production of these goods since they likely representworthwhile investment opportunities. As such, by modeling the demand andcost of a good and, thus, the profitability of a good, the systems,methods and computer program products of the present invention canfacilitate determining the value of the good and, in particular, thecontingent claim at the present time. For more information ondetermining the value of the project, see U.S. patent application Ser.No. 09/902,021 entitled: Systems, Methods and Computer Program Productsfor Performing a Generalized Contingent claim Valuation, filed Jul. 10,2001 and published on Jan. 16, 2003 as U.S. Patent ApplicationPublication No. 2003/0014337; and U.S. patent application Ser. No.10/453,396 entitled: Systems, Methods and Computer Program Products forModeling Uncertain Future Benefits, filed Jun. 3, 2003 and published onDec. 9, 2004 as U.S. Patent Application Publication No. 2004/0249642,the contents of both of which are hereby incorporated by reference inits entirety.

The systems, methods and computer program products of the presentinvention therefore are capable of modeling uncertain future demand,supply and associated profitability of a good over a period of timebased on sparse historical data or estimates regarding price andquantity of the good. By selecting a forecasted market for each segmentof the time period according to the Monte Carlo method based upon amarket potential distribution associated with the respective segment,embodiments of the present invention are capable of modeling uncertainfuture demand, supply and, thus the profitability as a function of thesize of the market within which the good is sold more adequately thanconventional methods of modeling the demand. Further, by including alognormal price sensitivity distribution, embodiments of the presentinvention are capable of modeling uncertain future demand, supply andassociated profitability for each segment of the time period whilebetter accounting for how changing the price of the good changes thenumber of units of the good purchased.

By accounting for variability, or uncertainty, in the price of the goodand the number of units of the good purchased over each time segment,embodiments of the present invention are capable of modeling uncertainfuture demand, supply and associated profitability over time to therebyfacilitate an understanding of how uncertainty in a market over timeaffects demand, supply and profitability. Such an understanding can beadvantageous to those associated with the manufacture, sale and purchaseof the good, such as in the context of commercial transactions. Programsfor the future sale of goods inherently have associated uncertainty,particularly as it relates to the market for the goods, typicallydefined by the number of good purchased and the price at which each unitof the good is purchased. According to embodiments of the presentinvention, for example, demand, supply and associated profitability of agood can be modeled in a manner such that a manufacturer can be in abetter position to not only decide whether to bring a good to market,but to also select a price at which to sell each unit of the good, aswell as a number of units of the good to produce.

As shown in FIG. 23, the system of embodiments of the present inventionis typically embodied by a processing element and an associated memorydevice, both of which are commonly comprised by a computer 60 or thelike. As indicated above, the method of embodiments of the presentinvention can be performed by the processing element manipulating datastored by the memory device with any one of a number of commerciallyavailable computer software programs. In one embodiment, the method canbe performed with data that is capable of being manipulated and/orpresented in spreadsheet form. For example, the method can be performedby the processing element manipulating data stored by the memory devicewith Excel, a spreadsheet software program distributed by the MicrosoftCorporation of Redmond, Washington, including Crystal Ball, a MonteCarlo simulation software program distributed by Decisioneering, Inc. ofDenver, Colo. The computer can include a display 62 for presentinginformation relative to performing embodiments of the method of thepresent invention, including the various distributions, models and/orconclusions as determined according to embodiments of the presentinvention. To plot information relative to performing embodiments of themethod of the present invention, the computer can further include aprinter 64.

Also, the computer 60 can include a means for locally or remotelytransferring the information relative to performing embodiments of themethod of the present invention. For example, the computer can include afacsimile machine 66 for transmitting information to other facsimilemachines, computers or the like. Additionally, or alternatively, thecomputer can include a modem 68 to transfer information to othercomputers or the like. Further, the computer can include an interface(not shown) to a network, such as a local area network (LAN), and/or awide area network (WAN). For example, the computer can include anEthernet Personal Computer Memory Card International Association(PCMCIA) card configured to transmit and receive information to and froma LAN, WAN or the like.

In one advantageous technique applicable to embodiments of the presentinvention, the methods according to embodiments of the present inventionmay be embodied in a software or data module, component, portfolio orthe like, that can be manipulated or otherwise operated within aspreadsheet software program such as Excel. Such a technique may beadvantageous in a number of different contexts, such as in the contextof financial modeling and analysis. Modules, components and/or portfoliothat perform various financial modeling functions can be combined togain a more complete understanding of a financial context. A briefdescription of such a technique as such may be applied to the presentinvention will now be described below.

According to such a technique, data capable of being manipulated toperform at least a portion of the methods of the present invention canbe embodied in a module, which can thereafter be linked or otherwiseassociated with other portions of the methods of the present inventionembodied in other modules so as to formulate a component. Then, if sodesired, the component can be linked or otherwise associated with othercomponents capable of performing other related methods to thereby form aportfolio. For example, methods of modeling future demand according toembodiments of the present invention can be embodied in one module whilemethods of modeling cost according to embodiments of the presentinvention can be embodied in another module. The two modules can then belinked or otherwise associated with one another to formulate a componentcapable of generating a business case capable of modeling theprofitability of the good based upon the future demand and cost. Then,if so desired, the component for generating the business case can belinked or otherwise associated with another component to perform anotherfunction.

According to one aspect of the present invention, the system of thepresent invention generally operates under control of a computer programproduct. The computer program product for performing the methods ofembodiments of the present invention includes a computer-readablestorage medium, such as the non-volatile storage medium, andcomputer-readable program code portions, such as a series of computerinstructions, embodied in the computer-readable storage medium. Itshould be understood that the computer-readable program code portionsmay include separate executable portions for performing distinctfunctions to accomplish methods of embodiments of the present invention.Additionally, or alternatively, one or more of the computer-readableprogram portions may include one or more executable portions forperforming more than one function to thereby accomplish methods ofembodiments of the present invention.

FIGS. 1 and 2 are a flowchart of methods, systems and program productsaccording to the invention. It will be understood that each block orstep of the flowchart, and combinations of blocks in the flowchart, canbe implemented by computer program instructions. These computer programinstructions may be loaded onto a computer or other programmableapparatus to produce a machine, such that the instructions which executeon the computer or other programmable apparatus create means forimplementing the functions specified in the flowchart block(s) orstep(s). These computer program instructions may also be stored in acomputer-readable memory that can direct a computer or otherprogrammable apparatus to function in a particular manner, such that theinstructions stored in the computer-readable memory produce an articleof manufacture including instruction means which implement the functionspecified in the flowchart block(s) or step(s). The computer programinstructions may also be loaded onto a computer or other programmableapparatus to cause a series of operational steps to be performed on thecomputer or other programmable apparatus to produce a computerimplemented process such that the instructions which execute on thecomputer or other programmable apparatus provide steps for implementingthe functions specified in the flowchart block(s) or step(s).

Accordingly, blocks or steps of the flowchart support combinations ofmeans for performing the specified functions, combinations of steps forperforming the specified functions and program instruction means forperforming the specified functions. It will also be understood that eachblock or step of the flowchart, and combinations of blocks or steps inthe flowchart, can be implemented by special purpose hardware-basedcomputer systems which perform the specified functions or steps, orcombinations of special purpose hardware and computer instructions.

Many modifications and other embodiments of the invention will come tomind to one skilled in the art to which this invention pertains havingthe benefit of the teachings presented in the foregoing descriptions andthe associated drawings. Therefore, it is to be understood that theinvention is not to be limited to the specific embodiments disclosed andthat modifications and other embodiments are intended to be includedwithin the scope of the appended claims. Although specific terms areemployed herein, they are used in a generic and descriptive sense onlyand not for purposes of limitation.

1. An apparatus comprising: a processor configured to define a pluralityof independent component markets for a good, wherein for each of thecomponent markets, the processor being configured to define thecomponent market includes being configured to: determine a pricesensitivity probability distribution of a price per unit of the good,the price sensitivity probability distribution assigning a respectiveprobability to each of a plurality of different predetermined prices perunit of the good, the price sensitivity probability distributionreflecting an uncertainty in the price per unit of the good, anddetermine a market potential probability distribution of a number ofunits of the good in the component market, the market potentialprobability distribution assigning a respective probability to each of aplurality of different numbers of units of the good, the marketpotential probability distribution reflecting an uncertainty in thenumber of units of the good in the component market, wherein theprocessor is also configured to generate a model of at least one ofdemand or supply for the good in an aggregate market formed of thecomponent markets, the processor being configured to generate the modelof at least one of demand or supply for the good in the aggregate marketfrom the price sensitivity probability distributions and marketpotential probability distributions of the component markets, wherein amodel of demand reflects a dependence between a quantity of the gooddemanded by consumers and a price per unit of the good in the aggregatemarket, and a model of supply reflects a dependence between a quantityof the good supplied to consumers and a price per unit of the good inthe aggregate market.
 2. An apparatus according to claim 1, wherein theprocessor being configured to generate a model of at least one of demandor supply for the good in an aggregate market includes being configuredto: generate a model of at least one of demand or supply for the good ineach of the component markets based upon respective price sensitivityprobability distributions and market potential probabilitydistributions; and combine the models of at least one of demand orsupply for the good to thereby generate a model of at least one ofdemand or supply for the good in an aggregate market formed of thecomponent markets.
 3. An apparatus according to claim 2, wherein themodels of at least one of demand or supply each include a plurality ofmarket segments having associated prices per unit, and wherein theprocessor being configured to combine the models includes beingconfigured to: rank the price per unit of each market segment across thecomponent markets in an ascending order or a descending order; calculatea cumulative number of units for each different price per unit, whereinthe calculated cumulative number of units for a price per unit equalsthe cumulative number of units having a price per unit less than therespective price per unit when the prices per unit are ranked inascending order, and wherein the calculated cumulative number of unitsfor a price per unit equals the cumulative number of units having aprice per unit no less than the respective price per unit when theprices per unit are ranked in descending order; and generate a model ofat least one of demand or supply for the good in an aggregate marketbased upon the different prices per unit and respective cumulativenumber of units.
 4. An apparatus according to claim 1, wherein theprocessor being configured to generate a model at least one of demand orsupply for the good in an aggregate market includes being configured to:determine a price sensitivity probability distribution for the aggregatemarket based upon a mean price and an associated standard deviation forthe aggregate market, the mean price and standard deviation having beencalculated based upon a price per unit of the good in each of thecomponent markets, the price per unit of the good in each of thecomponent markets having been determined based upon the pricesensitivity probability distributions and market potential probabilitydistributions of the respective component markets; determine a marketpotential probability distribution of a number of units of the good inthe aggregate market based upon a number of units of the good in each ofthe component markets, the number of goods in each of the componentmarkets having been determined based upon the market potentialprobability distributions of the respective component markets; andgenerate a model of at least one of demand or supply for the good in theaggregate market based upon the price sensitivity and market potentialprobability distributions for the aggregate market.
 5. A methodcomprising: defining a plurality of independent component markets for agood wherein for each of the component markets, defining the componentmarket comprises: determining a price sensitivity probabilitydistribution of a price per unit of the good, the price sensitivityprobability distribution assigning a respective probability to each of aplurality of different predetermined prices per unit of the good, theprice sensitivity probability distribution reflecting an uncertainty inthe price per unit of the good, and determining a market potentialprobability distribution of a number of units of the good in thecomponent market, the market potential probability distributionassigning a respective probability to each of a plurality of differentnumbers of units of the good, the market potential probabilitydistribution reflecting an uncertainty in the number of units of thegood in the component market; and generating a model of at least one ofdemand or supply for the good in an aggregate market formed of thecomponent markets, the model of at least one of demand or supply for thegood in the aggregate market being generated from the price sensitivityprobability distributions and market potential probability distributionsof the component markets, wherein a model of demand reflects adependence between a quantity of the good demanded by consumers and aprice per unit of the good in the aggregate market, and a model ofsupply reflects a dependence between a quantity of the good supplied toconsumers and a price per unit of the good in the aggregate market.
 6. Amethod according to claim 5, wherein generating a model of at least oneof demand or supply for the good in an aggregate market comprises:generating a model of at least one of demand or supply for the good ineach of the component markets based upon respective price sensitivityprobability distributions and market potential probabilitydistributions; and combining the models of at least one of demand orsupply for the good to thereby generate a model of at least one ofdemand or supply for the good in an aggregate market formed of thecomponent markets.
 7. A method according to claim 6, wherein the modelsof at least one of demand or supply each include a plurality of marketsegments having associated prices per unit, and wherein combining themodels comprises: ranking the price per unit of each market segmentacross the component markets in an ascending order or a descendingorder; calculating a cumulative number of units for each different priceper unit, wherein the calculated cumulative number of units for a priceper unit equals the cumulative number of units having a price per unitless than the respective price per unit when the prices per unit areranked in ascending order, and wherein the calculated cumulative numberof units for a price per unit equals the cumulative number of unitshaving a price per unit no less than the respective price per unit whenthe prices per unit are ranked in descending order; and generating amodel of at least one of demand or supply for the good in an aggregatemarket based upon the different prices per unit and respectivecumulative number of units.
 8. A method according to claim 5, whereingenerating a model of at least one of demand or supply for the good inan aggregate market comprises: determining a price sensitivityprobability distribution for the aggregate market based upon a meanprice and an associated standard deviation for the aggregate market, themean price and standard deviation having been calculated based upon aprice per unit of the good in each of the component markets, the priceper unit of the good in each of the component markets having beendetermined based upon the price sensitivity probability distributionsand market potential probability distributions of the respectivecomponent markets; determining a market potential probabilitydistribution of a number of units of the good in the aggregate marketbased upon a number of units of the good in each of the componentmarkets, the number of goods in each of the component markets havingbeen determined based upon the market potential probabilitydistributions of the respective component markets; and generating amodel of at least one of demand or supply for the good in the aggregatemarket based upon the price sensitivity and market potential probabilitydistributions for the aggregate market.
 9. A computer program productcomprising a computer-readable storage medium having computer-readableprogram code portions stored therein, the computer-readable programportions comprising: a first executable portion configured to define aplurality of independent component markets for a good, wherein for eachof the component markets, the first executable portion being configuredto define the component market includes being configured to: determine aprice sensitivity probability distribution of a price per unit of thegood, the price sensitivity probability distribution assigning arespective probability to each of a plurality of different predeterminedprices per unit of the good, the price sensitivity probabilitydistribution reflecting an uncertainty in the price per unit of thegood, and determine a market potential probability distribution of anumber of units of the good in the component market, the marketpotential probability distribution assigning a respective probability toeach of a plurality of different numbers of units of the good, themarket potential probability distribution reflecting an uncertainty inthe number of units of the good in the component market; and a secondexecutable portion configured to generate a model of at least one ofdemand or supply for the good in an aggregate market formed of thecomponent markets, the model of at least one of demand or supply for thegood in the aggregate market being generated from the price sensitivityprobability distributions and market potential probability distributionsof the component markets, wherein a model of demand reflects adependence between a quantity of the good demanded by consumers and aprice per unit of the good in the aggregate market, and a model ofsupply reflects a dependence between a quantity of the good supplied toconsumers and a price per unit of the good in the aggregate market. 10.A computer program product according to claim 9, wherein the secondexecutable portion being configured to generate a model of at least oneof demand or supply for the good in an aggregate market includes beingconfigured to: generate a model of at least one of demand or supply forthe good in each of the component markets based upon respective pricesensitivity probability distributions and market potential probabilitydistributions; and combine the models of at least one of demand orsupply for the good to thereby generate a model of at least one ofdemand or supply for the good in an aggregate market formed of thecomponent markets.
 11. A computer program product according to claim 10,wherein the models of at least one of demand or supply each include aplurality of market segments having associated prices per unit, andwherein the second executable portion being configured to combine themodels includes being configured to: rank the price per unit of eachmarket segment across the component markets in an ascending order or adescending order; calculate a cumulative number of units for eachdifferent price per unit, wherein the calculated cumulative number ofunits for a price per unit equals the cumulative number of units havinga price per unit less than the respective price per unit when the pricesper unit are ranked in ascending order, and wherein the calculatedcumulative number of units for a price per unit equals the cumulativenumber of units having a price per unit no less than the respectiveprice per unit when the prices per unit are ranked in descending order;and generate a model of at least one of demand or supply for the good inan aggregate market based upon the different prices per unit andrespective cumulative number of units.
 12. A computer program productaccording to claim 9, wherein the second executable portion beingconfigured to generate a model of at least one of demand or supply forthe good in an aggregate market includes being configured to: determinea price sensitivity probability distribution for the aggregate marketbased upon a mean price and an associated standard deviation for theaggregate market, the mean price and standard deviation having beencalculated based upon a price per unit of the good in each of thecomponent markets, the price per unit of the good in each of thecomponent markets having been determined based upon the pricesensitivity probability distributions and market potential probabilitydistributions of the respective component markets; determine a marketpotential probability distribution of a number of units of the good inthe aggregate market based upon a number of units of the good in each ofthe component markets, the number of goods in each of the componentmarkets having been determined based upon the market potentialprobability distributions of the respective component markets; andgenerate a model of at least one of demand or supply for the good in theaggregate market based upon the price sensitivity and market potentialprobability distributions for the aggregate market.